Question

Given Sin A = 5 /√34 and that angle A is in Quadrant I find the exact value of sec A in simplest radical form using a rational denominator

Answer 1

The given function is

`\sin A=\frac{5}{\sqrt[]{34}}`

We know that secA is the inverse of cosA.

From the given function, we form the following triangle

Because the sine function is equivalent to the ratio between the opposite leg and the hypotenuse.

So, let's use the Pythagorean's theorem to find y

`\begin{gathered} c^2=a^2+b^2 \\ (\sqrt[]{34})=y^2+5^2 \\ 34=y^2+25 \\ y^2=34-25 \\ y=\sqrt[]{9} \\ y=3 \end{gathered}`

Once we have the adjacent leg, we can express the cosine function

`\cos A=\frac{3}{\sqrt[]{34}}`

Then, the inverse is

`\sec A=\frac{\sqrt[]{34}}{3}`

Hence, the secA function is

`\sec A=\frac{\sqrt[]{34}}{3}`